N' Okaeme, P' Zanchetta, M' Sumner PEMC group University of Nottingham, UK

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N. Okaeme, P. Zanchetta, M. Sumner PEMC group
University of Nottingham, UK
ECON2 Marie Curie Mini-Conference  July 9, 2008,
School of EEE, University of Nottingham, UK
Automated Online Design of Robust Speed Digital
Controllers For Variable Speed Drives
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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Aim of the research
Traditional controllers such as Proportional plus
Integral (PI), which are widely used in
industrial drives, may not give satisfactory
results in all operative conditions, above all in
the presence of largely variable loads.
Keep straightforward control implementation
Provide excellent performance and robustness to
variable loads
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Aim of the research
To investigate a control design
procedure Robustness to variable loads and
different load types Traditional discrete linear
control implementation (z domain
controllers) (Most likely need higher order
controllers) No need for a fixed control
structure Automated design No need for plant
modelling
On-line optimization procedure for experimental
control system design using Genetic Algorithm (GA)
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Aim of the research
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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Genetic Algorithm
Stochastic global search method based on
biological evolution
GA

• Developed as a Part of Evolutionary Computing
  introduced in 1960s By I. Rechenberg
• GA proposed by John Holland in the mid-1970s
• Random Numerical Search and Optimisation
  Technique that operates on a population of
  potential solutions, termed individuals, applying
  the principle of evolution, simulated by means of
  mathematical operations that mimic the process of
  selection, crossover and mutation.
• A fitness function measures the fitness of an
  individual to survive in a population of
  individuals.

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Genetic Algorithm
Randomly Generate Initial Population
Yes
No
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Genetic Algorithm
Fitness function evaluation

• The quality of the system response to each load
  operative condition is quantified online using
  the Fitness function.
• The fitness function is defined as a linear
  function of the target specifications overshoot
  (OS), rise time (tr), steady state error (ess),
  steady state ripple (rss), system bandwidth (BW)
  - Further requirements can be added
• These indices are weighted individually and are
  summed up to give a fitness value. The overall
  quality of the closed loop response under
  different load conditions is obtained by
  weighting and then summing all of the relative
  fitness values
• FF (k1OS k2 tr k3 ess k4 rss k5
  BW)JJnom
• (k1OS k2 tr k3 ess k4 rss k5
  BW)J2Jnom

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Genetic Algorithm
Selection

• Process that chooses the fittest individuals from
  a population to continue into the next
  generation. Principle of Survival of the
  fittest
• Proportionate selection the probability that an
  individual advances to the next generation its
  proportional to its relative fitness
• Expected offsprings of an individual product of
  the individuals relative fitness times the
  number of individuals in the population.

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Genetic Algorithm
Crossover

• Crossover generates new individuals by exchanging
  genetic material between individuals
• Individual coding uses real number representation
• A random number between 0 and 1 is generated. If
  it is smaller than a fixed crossover probability
  then two individuals are randomly chosen and
  crossed. The resulting offspring replaces the
  parents in the new population.
• C1 and C2 parents individuals C1new and C2new
  offsprings
• C1new ? C1(1-?) C2
• C2new ? C2(1-?) C1
  0lt ?lt1 Crossover parameter

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Genetic Algorithm
Mutation

• Mutation effects a random variation upon the gene
  of an individual with a fixed mutation
  probability
• A random number between 0 and 1 is generated. If
  it is smaller than the mutation probability then
  a gene is randomly chosen and mutated. The
  resulting offspring replaces the parents in the
  new population
• Uniform Mutation
• Ci Ci1,., Cij ., Cin
  Individual
• Cinew Ci1,., Cijnew ., Cin
  New individual after mutation
• where Cijnew is a random value (with uniform
  probability distribution) within the domain of
  Cij

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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Digital Controller
Encoding unstructured controllers
e(k)
u(k)
F1
F2
F3
F4
F5
Chromosome of a single controller
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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Mechanical Loads Investigated

• Stiff shaft mechanical load
• J1 Jem 5J1 and B Bem 5B
• Flexible shaft mechanical load
• J2 JLem 5J2, D Dem 5D,
  backlash1.5rad/sec

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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Experimental Approach
Two identical permanent magnet DC servomotors
coupled along the same shaft. One serves as the
Driving motor and the other as the load motor.
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Experimental Approach
Power conversion stages DC to DC converter based
on a MOSFET H-Bridge configuration switching at
20kHz with nominal current of 5A Control xPC
target toolbox in Matlab-Simulink and interfaced
with the motors using the National Instrument
PCI-MIO-16XE-10 I/O board
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Experimental Approach

• GA based software that automatically designs
  optimised digital regulators for robust control
  of a permanent magnet DC variable speed drive has
  been developed
• Software applicable for control optimisation of
  power electronics and drives systems in general
• Optimisation of structure and parameters of
  speed controllers online, while the drive is
  being subject to variable mechanical loads.
• Different mechanical loads in the experimental
  control design tests are achieved by using a
  programmable load emulator.

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Experimental Approach

• High Flexibility Original Software tool in Matlab
• - every type of application and control
  structure
• - fitness function adjustable to specs
  requirements
• The software defines the more appropriate order
  and the best structure of the controller and
  determines the optimum values of its parameters
• Structure can include
• gain, pure integrator, PI regulator, real poles
  and zeros, complex poles and zeros
• The user can set
• - bounds for the parameters values
• - probability of mutation and crossover
• - guidance on the controller structure

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Summary on Experimental approach
Robust control design for loads with variable
inertia

• The GA software is written in Matlab language and
  runs on the host PC
• Each individual is then tested experimentally
  online on the actual real rig
• The speed closed loop dynamic for the range of
  different mechanical loads is measured

Host PC runs GA in Matlab

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Summary on Experimental approach

• Optimization time
• Optimisations are performed through 30
  generations with each generation having 40
  individuals Each experiment takes approximately
  5s. Total time for the optimisation is
  approximately two hours
• Experience has shown that improvements obtained
  with longer optimizations are not substantial for
  the sake of control robustness.

• Protections
• During the experiments, it is necessary to
  prematurely stop the experimental test of badly
  performing individuals (to reduce the time
  duration of the experiments, as well as the risks
  of damages to the hardware).
• Suitable logical protection schemes both in the
  control software and hardware implementation.

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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Background
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Identification of Nominal Model

• Offline simulation model
• Sub-optimal controller
• Model of mechanical loads
• Achieved using GA
• Run of 50 generations 50 individuals
• Identified over drives speed range
• Parameters identified at particular speeds
• Range of operation 0 3000 rpm
• Parameters values vs. speed plots
• Nominal model average of parameters

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Identification of Nominal Model

• Mechanical load with stiff shaft

Variation of the friction of the nominal load
Variation of the Inertia of the nominal load
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Identification of Nominal Model

• Mechanical load with stiff shaft

GA identified nominal model response matched with
experimental data reference speed 105 rad/s
GA identified nominal model response matched with
experimental data reference speed 210 rad/s
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Identification of Nominal Model

• Mechanical load with flexible shaft

Variation of the Inertia of the nominal load
Variation of Damping coefficient of nominal load
with speed
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Identification of Nominal Model

• Mechanical load with flexible shaft

Backlash causes oscillations reference speed
105 rad/s
reference speed 210 rad/s
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Plant Uncertainty Model

• Feedback Uncertainty Model for Gp is selected
• Models Unstructured Uncertainty
• Poles crossing from left right-half plane

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Plant Uncertainty Model

• Define weighting function, W2

Load with flexible Shaft W2 0.002(0.004s 1)
Load with Stiff Shaft W2 0.00075(0.325s 1)
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Performance criteria

• Robust stability condition
• Where S is
• and C is the controller
  transfer function

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Closed loop control design

• Optimization implemented using GA
• Offline model of experimental system
• Fitness function
• Nominal performance Robust Stability

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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Results

• GA designed controller response

Load with Stiff Shaft Inertia 5J, Friction
5B Tr 100ms, Ts 110ms
Load with Stiff Shaft Inertia J, Friction
5B Tr 50ms, Ts 55ms
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Results

• GA designed controller response

Load with flexible shaft with backlash Inertia
5J, Damping 5D Tr 60ms, Ts 65ms
Load with flexible shaft with backlash Inertia
J, Damping 5D Tr 52ms, Ts 57ms
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Outline

• Aim of the research

• Genetic Algorithm
• Digital Controller
• Mechanical Loads Investigated
• Experimental Approach
• Theoretical Approach
• Results
• Conclusion

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Conclusion

• Simple effective approach
• Reduces commissioning time for drives
• Requires little user interaction
• Experimental robust control design
• Does not require modelling
• Optimization implemented directly on rig
• Theoretical robust control design
• Faster implementation within computer
• Less stress experienced by load machine